Blackwell Science, LtdOxford, UKPCEPlant, Cell and Environment0016-8025Blackwell Science Ltd 2003? 2003
26?13431356
Original Article
Leaf ‘hydrology’
L. Sack
et al.
Plant, Cell and Environment (2003) 26, 1343–1356
The ‘hydrology’ of leaves: co-ordination of structure and
function in temperate woody species
L. SACK1,2,3, P. D. COWAN2, N. JAIKUMAR1 & N. M. HOLBROOK1
1
Harvard University, Department of Organismic and Evolutionary Biology, Biological Laboratories, 16 Divinity Avenue,
Cambridge, Massachusetts 02138, USA, 2Harvard Forest, PO Box 68, 324 N. Main Street, Petersham, Massachusetts 01366
USA and 3The Arnold Arboretum of Harvard University, 125 Arborway, Jamaica Plain, Massachusetts 02130, USA
ABSTRACT
The hydraulic conductance of the leaf lamina (Klamina) substantially constrains whole-plant water transport, but little
is known of its association with leaf structure and function.
Klamina was measured for sun and shade leaves of six woody
temperate species growing in moist soil, and tested for correlation with the prevailing leaf irradiance, and with 22
other leaf traits. Klamina varied from 7.40 ¥ 10-5 kg m-2
s-1 MPa-1 for Acer saccharum shade leaves to 2.89 ¥
10-4 kg m-2 s-1 MPa-1 for Vitis labrusca sun leaves. Tree sun
leaves had 15–67% higher Klamina than shade leaves. Klamina
was co-ordinated with traits associated with high water flux,
including leaf irradiance, petiole hydraulic conductance,
guard cell length, and stomatal pore area per lamina area.
Klamina was also co-ordinated with lamina thickness, water
storage capacitance, 1/mesophyll water transfer resistance,
and, in five of the six species, with lamina perimeter/area.
However, for the six species, Klamina was independent of
inter-related leaf traits including leaf dry mass per area,
density, modulus of elasticity, osmotic potential, and cuticular conductance. Klamina was thus co-ordinated with structural and functional traits relating to liquid-phase water
transport and to maximum rates of gas exchange, but independent of other traits relating to drought tolerance and to
aspects of carbon economy.
Key-words: hydraulic architecture; hydraulic conductivity;
hydraulic resistance; leaf water storage; specific leaf area;
stomatal conductance.
INTRODUCTION
Leaves vary tremendously in their area, thickness, shape,
and in their capacities for gas exchange and for withstanding drought. This diversity is generated by phylog-
Correspondence: Lawren Sack, Harvard University, Department of
Organismic and Evolutionary Biology, Biological Laboratories, 16
Divinity Avenue, Cambridge, Massachusetts 02138 USA. Fax:
+1 617 496 5854; e-mail: [email protected]
© 2003 Blackwell Publishing Ltd
eny and adaptation but constrained by trait correlations.
Recently, important headway has been made in elucidating leaf trait correlations relating to carbon economy (e.g.
Field & Mooney 1986; Reich, Walters & Ellsworth 1997;
Reich, Ellsworth & Walters 1998; Reich et al. 1999;
Wright, Reich & Westoby 2001). The aim of this study is
to test analogous links among leaf traits relating to water
balance.
The hydraulic properties of the leaf lamina, the terminal
component of the transpiration stream, significantly constrains whole-plant hydraulic conductance (Kplant). Kplant
defines the capacity of a plant for water use. In a given
microclimate and soil water supply, it is the stomatal and
boundary-layer conductances that determine the transpiration rate, while Kplant determines the leaf water potential at
that transpiration rate (Cowan 1972; Tyree & Zimmermann
2002). Kplant thus defines how high stomatal conductance
may be without desiccating the leaf, and often correlates
with maximum stomatal conductance within and across
species (Kuppers 1984; Meinzer & Grantz 1990; Nardini,
Tyree & Salleo 2001; Bhaskar et al. 2002). Values in the
literature suggest that the leaf lamina hydraulic conductance (Klamina) scales linearly with Kplant, with an allometric
constant of ª 4 (Fig. 1); that is Klamina is ª 4 ¥ Kplant. Stated in
another way, leaf hydraulic resistance accounts for onequarter of the whole-plant resistance.
Klamina is determined by the vascular and extra-vascular
pathways of transpired water (Yang & Tyree 1994; Nardini
et al. 2001; Sack et al. 2002). Water enters the leaf through
the petiole and flows through orders of veins in series and
parallel, across the bundle sheath, and into and/or around
the mesophyll cells, before evaporation into airspaces and
diffusion out of the stomata. We tested whether Klamina was
linked with 22 other leaf traits, and with the prevailing leaf
irradiance. Given the hydraulic importance of Klamina we
hypothesized it would be associated with leaf traits relating to water flux, such as petiole hydraulic conductance
and stomatal size and/or density. We also tested whether
Klamina was linked with traits associated with aspects of
drought tolerance including pressure–volume curve
parameters (Abrams 1988; Niinemets 2001), and cuticular
conductance.
1343
1344 L. Sack et al.
neously in an open area (using matched quantum sensors;
LI-250 Light Meter; Li-Cor Inc., Lincoln, NE, USA), for
calculation of the percentage daylight diffuse PAR
(Anderson 1964).
Leaf lamina and petiole hydraulic conductance
Figure 1. The scaling of leaf lamina and whole-plant hydraulic
conductance, for 34 species; filled triangles represent herbs, filled
circles woody seedlings and saplings, and open circles mature trees
and shrubs (Klamina determined using high-pressure flow meter;
Kplant using various methods; data of Becker, Tyree & Tsuda 1999;
Nardini & Tyree 1999; Nardini et al. 2000; Nardini & Salleo 2000;
Tsuda & Tyree 2000). Standard major axis ± 95% confidence intervals of log–log data =1.21 ± 0.22.
MATERIALS AND METHODS
Plant material
Six species were sampled that had leaves with obvious differences in thickness, texture, and apparent desiccation tolerance. From June to August 2001 at Harvard Forest in
Petersham, MA (42¢54∞ N, 72¢18∞ W) trees were selected of
Acer rubrum Marsh. (Aceraceae; nomenclature follows
Gleason & Cronquist 1991), Acer saccharum Marsh., Betula papyrifera L. (Betulaceae) and Quercus rubra L.
(Fagaceae), growing at exposed sites or along roads and
trails within the forest. Diameters at breast height ranged
between 0.16 and 0.39 m (A. rubrum), 0.56–0.91 m (A. saccharum), 0.07–0.10 m (Betula) and 0.20–0.51 m (Quercus).
Shoots were sampled 5–8 m above the ground, from the
exposed part of the canopy (‘sun leaves’), and the canopy
interior (‘shade leaves’) of five trees per species. Shoots of
Hedera helix L. (Araliaceae) and Vitis labrusca L. (Vitaceae) were collected from one or several individuals that
covered more than 30 m of fence at the Harvard Forest
(Vitis), or from large vines growing along a fence at the
Harvard University campus (Hedera, sampled in October).
Material collected in the field was re-cut under water and
allowed to hydrate overnight by placing the cut ends of the
shoots in water, and covering leaves with plastic. A 10 mM
aqueous KCl solution was used to hydrate the samples to
be used in hydraulic measurements, identical to the solution used for those measurements.
The prevailing light environments of the sampled leaves
were measured. On overcast days the photosynthetically
active radiation (PAR) incident on the leaf was measured
for five experimental leaves on each plant, and simulta-
Klamina values and petiole conductances for the tree sun
leaves, and for Hedera and Vitis, are reported in a previous
study (Sack et al. 2002), with additional data for tree shade
leaves collected during the same period. The three methods
for determining Klamina compared by Sack et al. (2002)
involve driving water flow through excised leaves, and
simultaneously determining the pressure gradient driving
the flow; Klamina is calculated as the ratio of flow rate to
pressure gradient. The three methods gave statistically similar results and the data were pooled for this study. Measurements of tree shade leaves were made using two of the
three methods described in Sack et al. (2002), the ‘evaporative flux method’, and the ‘vacuum pump method’ (after
methods described in Kolb, Sperry & Lamont 1996; Nardini
et al. 2001); n = 5–7 per species per method (1–2 leaves from
each study tree). The values provided by the two methods
were also statistically indistinguishable in a two-way analysis of variance (log-transformed Klamina values, with factors
species and method; P < 0.001 for species; P = 0.33 for
method; P = 0.88 for species–method interaction), and were
pooled for each species. Petiole conductance was measured
for shade leaves using methods described by Sack et al.
(2002), driving flow through petiole segments at a determined positive pressure, with n = 5–8 per species. Hydraulic
measurements were made in ambient temperatures of
23 ± 2 ∞C; for leaves that heated above ambient during
measurement (by up to 2 ∞C), Klamina was reduced by 2%
per ∞C above ambient, to normalize for the effects of temperature on viscosity (see Sack et al. 2002).
Petiole hydraulic conductance was normalized to leaf
dimensions in two ways. Petiole conductivity (kpetiole;
units, kg s-1 m MPa-1) was calculated as petiole
conductance ¥ petiole length, and petiole conductance per
leaf area (Kpetiole; units, kg s-1 m-2 MPa-1) as petiole conductance/lamina area. Lengths of whole petioles were estimated from known lamina areas, using petiole length
versus lamina area regressions for each leaf type (R2 = 0.40–
0.75; P < 0.05; Table 1). For these regressions, sun and
shade shoots were sampled from four to five study trees per
species, and three to four shoots were sampled from each
climber species. From each shoot, the largest and smallest
leaves, and one or two average-sized leaves, were sampled.
For each leaf type, this sampling protocol resulted in 10 to
16 leaves evenly spread over the typical size range.
Leaf form and composition
Leaf form and composition were measured for each leaf
type. Two sun and two shade leaves from each tree were
sampled for each measurement, and two leaves from each
of five different shoots of Hedera and Vitis; the two values
© 2003 Blackwell Publishing Ltd, Plant, Cell and Environment, 26, 1343–1356
© 2003 Blackwell Publishing Ltd, Plant, Cell and Environment, 26, 1343–1356
0.90 ± 0.08
0.75 ± 0.09
1.3 ± 0.20
1.2 ± 0.15
0.52 ± 0.05
0.64 ± 0.04
1.4 ± 0.25
2.3 ± 0.18
2.6 ± 0.14
4.2 ± 0.22
64 ± 4.8
6.3 ± 1.1
39 ± 3.3
2.0 ± 0.18
46 ± 1.6
12 ± 0.92
14 ± 0.27
58 ± 3.1
7.4 ± 0.82
60 ± 3.7
8.71 ± 1.30†
0.60***
6.81 ± 1.40†
0.44***
3.40 ± 0.64†
0.54***
10.3 ± 2.6
0.62**
1.73 ± 0.27†
0.75***
4.86 ± 1.51
0.40**
a ± SE
R2
2.89 ± 0.25 (12)
1.59 ± 0.21 (15)
1.44 ± 2.16 (15)
4.56 ± 1.49 (10)
1.16 ± 0.24† (24)
2.82 ± 0.79† (30)
1.92 ± 0.71† (30)
b (¥ 10 ) ± SE (n)
-2
7.38 ± 1.56†
0.61***
3.60 ± 0.38†
0.90***
9.58 ± 1.46†
0.82***
7.49 ± 1.69
0.73**
34.0 ± 3.52†
0.79***
16.2 ± 5.79
0.53*
-4.33 ± 2.92 (21)
-11.7 ± 2.24 (5)
-11.7 ± 11.3 (7)
-1.1 ± 0. 86 (12)
-3.2 ± 0.50 (5)
-0.29 ± 0.18 (6)
-1.08 ± 0.14 (5)
-0.44 ± 0.34 (5)
-1.02 ± 0.20 (5)
-1.7 ± 0.96 (8)
0.781 ± 0.020 (16)
0.703 ± 0.020 (16)
0.545 ± 0.021 (13)
0.660 ± 0.020 (15)
0.575 ± 0.020 (15)
0.605 ± 0.029 (15)
0.580 ± 0.020 (16)
0.606 ± 0.020 (17)
0.542† ± 0.018 (17)
b ± SE (n)
a (¥ 10-5) ± SE
R2
b (¥ 10-7) ± SE (n)
Log lamina
perimeter (cm)
vs lamina area (m2)
kpetiole (¥ 10-5 kg s-1 m-1 MPa-1)
vs log lamina area (cm2)
Significance levels: *P £ 0.05; **0.01 > P ≥ 0.001; ***P £ 0.001. For regressions of petiole length and kpetiole versus lamina area, species’ regressions differed in slopes (F-ratio tests; P < 0.001);
for log lamina perimeter versus log lamina area, all leaf types shared a common slope (0.52 ± 0.0175 SE, R2 = 0.92, P < 0.001), and differed significantly in intercepts (F-ratio tests; P < 0.001).
†Common slope or intercept for sun and shade leaves.
Vitis labrusca
Quercus rubra
Hedera helix
Betula papyrifera
Sun
Shade
Sun
Sun
Shade
Sun
Shade
Sun
Shade
Shade
Acer rubrum
Acer saccharum
Sun/shade
Species
Lamina volume
(cm3)
Mean dsf ± SE
(% daylight)
Petiole length (m) vs lamina
area (m2)
Table 1. Mean values ± standard error for the diffuse site factors (dsf) and volumes of sun and shade leaves of each species (n = 10–25 for each leaf type) and for parameters (slopes a and
intercepts b) of the linear regressions of petiole length, petiole conductivity (kpetiole), and lamina perimeter versus area
Leaf ‘hydrology’ 1345
1346 L. Sack et al.
for each tree or shoot were averaged, resulting in n = 5 for
each leaf type. The leaves were hydrated overnight (as
described above), weighed (for ‘turgid mass’), and then
placed in a vacuum flask containing distilled water, and
vacuum-infiltrated >4 h. When the leaves were infiltrated
and hyaline, they were towelled dry, weighed again (for
‘infiltrated mass’), and then lamina volume was determined
by water displacement in a graduated cylinder, to the nearest 0.05 cm3, after which lamina area was determined (LiCor leaf area meter; Li-Cor Inc.). Leaf laminas were
weighed again after drying at 70 ∞C for > 72 h (for ‘dry
mass’). From these measurements, the air–water–dry matter volumetric fractions were determined: volumes of lamina air and water were determined, respectively, as
infiltrated mass - turgid mass and as turgid mass - dry mass
(using the density of liquid water =1000 kg m-3); volume of
dry matter was determined as lamina volume – volumes of
air and water; volumetric fractions were determined dividing by lamina volume (cf. Roderick et al. 1999a). Leaf density was determined as lamina dry mass/lamina volume. The
density of the dry matter was determined as dry mass/
volume of dry matter. Lamina thickness was determined as
lamina volume/lamina area. Leaf dry mass per area (LMA)
was determined as lamina area/lamina dry mass; it is also
equal to lamina thickness ¥ density (Witkowski & Lamont
1991).
Leaf outline was characterized both as perimeter/area
(Talbert & Holch 1957) and perimeter2/area (cf. McLellan
& Endler 1998). Leaves for shape analysis were sampled
according to the same protocol as described above for the
regressions of petiole length versus lamina area. Each leaf
was digitally scanned (using an Epson ES-1200C scanner;
Epson, Long Beach, CA, USA), and the perimeter and
area determined using image analysis software (ImageJ,
public domain software; http://rsb.info.nih.gov/ij/). For each
leaf type, log perimeter was regressed against log lamina
area, because perimeter and area were found to follow a
geometric power law scaling; that is, perimeter increased in
proportion with the square root of area for leaves of each
type. Perimeter/area was estimated from the regressions for
leaves of mean lamina area (Zar 1999). Because perimeter2/
area is independent of leaf size, a mean value for each leaf
type was calculated based on all leaves sampled for shape.
Stomatal density, guard cell length and stomatal
pore area index
Stomatal densities and guard cell lengths were determined
by microscopic measurement of impressions from abaxial
nail varnish peels taken centrally, midway between midrib
and margin. This method could not be used for the papillate
Vitis leaf; for this species, leaves were gently macerated, and
sections of abaxial epidermis were removed and inverted
(following Grubb, Grubb & Miyata 1975), and microscopic
measurements were made on these sections. Counts were
averaged for four locations per peel; peels were made for
one sun and one shade leaf for each study tree, from two
leaves from each of five shoots of Hedera and one leaf from
each of three shoots of Vitis. Total stomatal pore area index
(SPI; a dimensionless index of stomatal pore area per lamina area) was calculated as stomatal density ¥ guard cell
length2.
Pressure–volume curve parameters and water
storage capacitance
Pressure–volume curve parameters were determined for
one sun and one shade leaf from each tree, and one leaf
from each of five shoots of Hedera and Vitis. The leaves
were dried on a laboratory bench, and alternately weighed
and measured for water potential with a pressure chamber
(PMS Instrument Co., Corvallis, OR, USA). Subsequently
dry mass was determined after more than 72 h at 70 ∞C.
Pressure–volume curve parameters were calculated (Koide
et al. 2000): osmotic potential at full turgor and at the turgor
loss point (pft and ptlp), modulus of elasticity at full turgor
(Œft), and relative capacitance at full turgor (Cft; DRWC/D
leaf water potential, between full turgor and turgor loss
point). ‘Plateau’ effects’ associated with leaf airspace infiltration were found for some of the leaves, and corrected
(Kubiske & Abrams 1991). For parameters calculated from
slopes of two ‘dependent variables’, i.e. for Œft and Cft,
standard major axes were used (Sokal & Rohlf 1995). Leafarea specific capacitance was calculated as Cft ¥ (lamina turgid mass - lamina dry mass)/lamina area, using mean values (Cft*, in units of kg MPa-1 m-2). The transfer resistance
(Rt) linking water stored in mesophyll cells with the vasculature was measured following the method described by
Nobel & Jordan (1983). In this method, the kinetics of the
decline of water potential were followed for leaves repeatedly pressurized for 2 s to 0.2 MPa above turgid water
potential, in a pressure bomb (Nobel & Jordan 1983). Analysing the kinetics yields the time constant for water
exchange (t1/2). Rt was calculated assuming that t1/2 is equal
to Rt ¥ Cft*. Standard errors for Cft* and Rt were determined by propagation of error (Beers 1957).
Cuticular conductance
Cuticular conductance (= ‘minimum conductance’, gmin
sensu Kerstiens 1996) was determined for one sun and one
shade leaf from each tree, and one leaf from each of five
shoots of Hedera and Vitis. Hydrated leaves were dried on
a laboratory bench, at PAR < 10 mmol photons m-2 s-1, for
6–8 h. The leaves were weighed at intervals of 10–30 min.
Cuticular transpiration was measured as the slope of water
loss versus time; the slope often became shallower within
the first hour of drying, suggesting progressive stomatal
closure, followed by a highly linear decline for hours
(R2 > 0.995), suggesting closed stomata; the slope of the
decline from 2 to 4 h was used to estimate cuticular transpiration. The value of gmin was calculated as cuticular transpiration/mole fraction gradient in water vapour from the
leaf to air, assuming the leaf internal air to be fully saturated (Pearcy, Schulze & Zimmermann 2000). Ambient
temperature and relative humidity (RH), measured at
© 2003 Blackwell Publishing Ltd, Plant, Cell and Environment, 26, 1343–1356
Leaf ‘hydrology’ 1347
30 min intervals (LI-1600; LiCor Inc.), fluctuated minimally
during the measurements (i.e. respectively, ± 1 ∞C and
±0.5–2%). Mean temperature and RH during measurement were 22 ∞C and 35% for Acer spp. and Quercus, 22 ∞C
and 45% for Betula and Vitis and 25 ∞C and 12.5% for
Hedera. The differences in RH for measurement of different species were not in the range that would significantly
affect gmin (Schreiber et al. 2001).
Statistics
Species and sun–shade differences were determined using
two-way ANOVAs after log-transformation of data to
increase heteroscadicity and to model for multiplicative
effects (Minitab Release 13.32; Minitab Inc., State College,
PA, USA). Relationships between petiole conductivity and
petiole length versus lamina area, and between log lamina
perimeter and log lamina area were determined using
regression analyses. The regressions for each species’ sun
and shade leaves were compared; when slopes were the
same, tests were made for differences in intercepts (using
Genstat 5th edition; Zar 1999). Similarly, different species’
regressions were compared.
For leaf traits, parametric correlation and Spearman
rank-correlation coefficients (rp and rs; Sokal & Rohlf 1995)
were calculated using Minitab Release 13.32. We confirmed
that correlations between lamina area-normalized variables
were not due to auto-correlation (Niklas 1994), by testing
again after removing the area dependence of one or both
variables by multiplying or dividing by lamina area.
Allometric relationships were determined using standard
major axes and rp for log-transformed data (Sokal & Rohlf
1995). Standard errors were calculated as for ordinary linear regression (Niklas 1994; Sokal & Rohlf 1995).
RESULTS
Comparisons of tree sun and shade leaves
Tree sun leaves had significantly higher Klamina than shade
leaves (Fig. 2; Table 2), strikingly in A. saccharum (sun
leaves 67% higher), and in Q. rubra (48% higher). Petiole
hydraulic conductance was also higher for sun leaves. For
each species petiole conductivity (kpetiole, conductance ¥
petiole length, in kg m s-1 MPa-1) was linearly related to
lamina area (R2 = 0.53–0.90; P < 0.05; Table 1). The regressions of kpetiole versus lamina area coincided in slope for sun
and shade leaves of each species, with the sun leaves having
higher intercepts (F-ratio tests; P < 0.05; Table 1). As the
leaves of larger lamina area have longer petioles (Table 1),
for each leaf type petiole conductance per leaf area (Kpetiole;
conductance/lamina area, in kg m-2 s-1 MPa-1) was invariant
with leaf size (i.e. no significant trend with increasing leaf
area). Kpetiole was significantly higher for sun than shade
leaves (up to 2.3 ¥ higher, for A. rubrum; Table 2; Fig. 2).
The differences in Klamina, kpetiole and Kpetiole coincided with
previously characterized sun–shade differences in other
traits (e.g. Givnish 1988; Abrams & Kubiske 1990;
Figure 2. Co-ordination of petiole and lamina hydraulic conductance. Open symbols, sun leaves; filled symbols, shade leaves. Species symbols and n for Klamina (sun/shade): Ar, Acer rubrum, 16/11;
As, Acer saccharum, 18/12; Bp, Betula papyrifera, 16/10; Hh, Hedera helix 16; Qr, Quercus rubra 24/10; Vl, Vitis labrusca, 18. nvalues for Kpetiole as for kpetiole (Table 1). Error bars = 1 SE. Significance levels as in Table 1.
Niinemets & Kull 1994) as well as with several sun–shade
differences that are novel. Sun leaves were smaller and
thicker than shade leaves (Fig. 3a & b; Table 2); the two
effects compensated, leading to a similar lamina volume
(Tables 1 & 2). Sun leaves generally had higher perimeter/
area than shade leaves (Table 2), up to 36% greater, for
Quercus (Fig. 3d), and higher stomatal pore area index, up
to 54% higher, again in Quercus, due to higher stomatal
densities, because guard cell length was statistically similar
(Fig. 4a–c). Sun leaves had lower (i.e. more negative) ptlp
than shade leaves and, in three of four tree species, higher
pft and lower Rt (Fig. 5a & d).
Sun leaves were denser than shade leaves, with a significantly smaller volumetric fraction of air (Fig. 6a & b), a
difference balanced by their slightly (and non-significantly)
higher volumetric fraction of water and/or dry matter
(Fig. 6a, Table 2). Sun leaves also had denser dry matter in
each species but A. rubrum (Fig. 6c; Table 2). With their
greater thickness and density, sun leaves had ~10% to
110% higher LMA than shade leaves (Fig. 6b; Table 2). In
A. saccharum and Quercus, sun leaves had lower gmin than
shade leaves (Fig. 6d).
Comparisons across all leaf types
Klamina: variation and linkage with prevailing leaf
irradiance
Klamina values varied approximately four-fold, ranging from
7.40 ¥ 10-5 kg m-2 s-1 MPa-1 for A. saccharum shade leaves
to 2.89 ¥ 10-4 kg m-2 s-1 MPa-1 for Vitis sun leaves (Fig. 2).
Klamina rank-correlated with leaf irradiance (P < 0.05), which
ranged from 2% daylight for A. saccharum shade leaves to
64% daylight for A. rubrum sun leaves (Tables 1 & 3).
© 2003 Blackwell Publishing Ltd, Plant, Cell and Environment, 26, 1343–1356
1348 L. Sack et al.
Table 2. Mean squares and significance of effects in analyses of variance for individual leaf traits
One-way ANOVA testing for
species differences, using sun
leaves for trees
Two-way ANOVA testing for species differences and sun–shade
differences, for the four tree species
Trait
Species
(d.f. = 5)
Error mean
squares (d.f.)
Species
(d.f. = 3)
Sun–shade
(d.f. = 1)
Species ¥ Sun–shade
(d.f. = 3)
Error mean
squares (d.f.)
Klamina
Kpetiole
Lamina volume
Lamina area
Lamina thickness
Perimeter2/area
Stomatal density
Guard cell length
Stomatal pore area index
Relative Cft
t1 /2
Lamina density
LMA
Vol fraction air
Vol fraction water
Vol fraction dry matter
Density of dry matter
Œft
pft
ptlp
gmin
0.361***
3.04***
0.506***
0.354***
0.262***
0.582***
0.375***
0.200***
0.233**
0.111**
0.100***
0.0968***
0.0381***
0.278***
0.00734**
0.109***
0.0250
0.160***
0.0662***
0.0388***
0.941***
0.0372 (102)
0.0115 (53)
0.0127 (24)
0.0109 (24)
0.00326 (24)
0.00755 (87)
0.00458 (27)
0.0100 (27)
0.0510 (27)
0.0273 (24)
0.00526 (24)
0.00247 (24)
0.00558 (24)
0.000657 (24)
0.00175 (24)
0.0103 (24)
0.0116 (24)
0.0161 (24)
0.00642 (24)
0.00295 (24)
0.00748 (24)
0.946***
4.25***
0.721***
0.695***
0.0324***
1.02***
1.10***
0.656***
0.638***
0.142***
0.204***
0.0633***
0.0781***
0.340***
0.0201***
0.0470**
0.0380**
0.246***
0.128***
0.0929***
0.132***
0.493***
0.816***
0.00015
0.0756**
0.0788***
0.00010
0.0214*
0.00397
0.0741**
0.0276
0.001
0.101***
0.359***
0.143***
0.00216
0.00591
0.0612*
0.131*
0.0544**
0.0575***
0.0023
0.0364
0.0169
0.0163
0.00315
0.0120**
0.0882***
0.00459
0.00170
0.0164
0.0688
0.0261*
0.00736
0.0374**
0.0136
0.00470
0.0302*
0.0167
0.0484
0.0452**
0.00145
0.0248
0.0268 (109)
0.0090 (56)
0.0101 (32)
0.00812 (32)
0.00226 (32)
0.0138 (120)
0.00451 (32)
0.00152 (32)
0.00871 (32)
0.0174 (32)
0.00676 (32)
0.00360 (32)
0.00641 (32)
0.00653 (32)
0.00213 (32)
0.00696 (32)
0.00840 (32)
0.0270 (32)
0.00702 (32)
0.00343 (32)
0.0108 (32)
LMA, leaf dry mass per area. *P <0.05; ** 0.01 ≥ P > 0.001; ***P £ 0.001.
Petiole hydraulics and Klamina
Kpetiole differed approximately 26-fold, from A. saccharum
shade leaves to Quercus sun leaves (Fig. 2). Kpetiole was
rank-correlated with Klamina (Fig. 2; Table 3). The absence of
a parametric correlation between Kpetiole and Klamina (Fig. 2;
Table 3) means that the percentage of the area-normalized
leaf resistance accounted for by the petiole varies significantly, from 4% in Quercus sun and shade leaves to 34%
in Hedera (median for all leaf types, 19%).
Lamina dimensions and Klamina
The study leaves differed significantly in size and shape: by
approximately six-fold in area, two-fold in thickness, eightfold in volume, three-fold in perimeter2/area, and two-fold
in perimeter/area (Fig. 3a–d; Tables 1 & 2). Klamina was independent of lamina area (Fig. 3b), volume, perimeter2/area
(Fig. 3c) and of perimeter/area (Fig. 3d), but significantly
correlated with lamina thickness (Fig. 3a; Table 3); analysed allometrically, Klamina µ lamina thickness1.75 ± 0.46 SE (rp =
0.67; P = 0.034). In addition, excluding Vitis, Klamina correlated with perimeter/area for the remaining five species
(Fig. 3d).
Leaf stomatal traits and Klamina
Stomatal density varied approximately six-fold, from 82 per
mm2 in Betula shade leaves to 494 per mm2 in Quercus sun
leaves, and guard cell length varied approximately fourfold, from 10 mm in A. rubrum to 42 mm in Betula (Fig. 4a
& b; Table 2). Stomatal density correlated negatively with
guard cell length (Table 3). Analysed allometrically, stomatal density µ guard cell length-1.3 ± 0.25 SE (rp = -0.85;
P = 0.002). This relation is not sufficiently compensatory as
to equalize stomatal pore area index (SPI, the product of
stomatal density and guard cell length2); the study leaves
differed by approximately six-fold (Fig. 4c; Table 2). Differences in SPI were driven by differences in guard cell length
(rp = 0.68; P = 0.03), rather than by differences in stomatal
density (rs = -0.15; P = 0.68; rp = -0.28; P = 0.43). Klamina was
uncorrelated with stomatal density (Fig. 4a), rankcorrelated with guard cell length (Fig. 4b; Table 3), and
tightly correlated with SPI (rp = 0.93; P < 0.001; Fig. 4c;
Table 3). Analysed allometrically, Klamina µ guard cell
length0.83 ± 0.22 SE (rp = 0.64; P = 0.044), and Klamina µ SPI0.74 ± 0.08
SE (
rp = 0.95; P < 0.001).
Leaf water storage traits and Klamina
Both relative capacitance (Cft) and leaf-area specific capacitance (Cft*) varied approximately four-fold, time constants
approximately 2.5-fold, and transfer resistance (Rt) approximately seven-fold (Table 2; Fig. 5a–d). Cft* was negatively
related to Rt (rs = 0.84; P = 0.002; rp = 0.67; P = 0.033). Notably, Klamina was unrelated to Cft, but positively correlated
with Cft* (Fig. 5b); Klamina was correlated with water mass
© 2003 Blackwell Publishing Ltd, Plant, Cell and Environment, 26, 1343–1356
Leaf ‘hydrology’ 1349
per unit area, which contributed strongly to species differences in Cft*, as reported for three desert species (Nobel &
Jordan 1983). Klamina correlated negatively with Rt (Fig. 5d;
Table 3). As Rt might represent a component of the overall
lamina hydraulic resistance (the inverse of Klamina; see Discussion), Rt was considered as a percentage of 1/Klamina. Rt
accounted for 14% of the lamina hydraulic resistance in
Vitis and for 60% in Hedera, but for most leaves was close
to the median value, 28%.
Traits associated with leaf drought tolerance
Leaves varied significantly in composition (Fig. 6a,
Table 2), and in parameters associated with leaf drought
Figure 3. Co-ordination of Klamina and leaf dimensions: (a) lamina
thickness; (b) area; (c) perimeter2/area; and (d) perimeter/area.
Symbols as in Fig. 2; in (d), vertical error bars are 95% confidence
intervals.
Figure 4. Co-ordination of Klamina and stomatal traits: (a) stomatal density; (b) guard cell length; and (c) total stomatal pore
area index. Symbols as in Fig. 2.
© 2003 Blackwell Publishing Ltd, Plant, Cell and Environment, 26, 1343–1356
1350 L. Sack et al.
an exceptionally low value (cf. median value of approximately 3 mmol m-2 s-1 for more than 100 species; Kerstiens
1996). Klamina was independent of leaf volumetric composition, density, and LMA, and of traits associated with leaf
drought tolerance, Œft, pft, ptlp, and gmin. However, there were
notable correlations among these traits, independent of
Klamina. Leaf density was strongly positively linked with volumetric fraction of dry matter, and negatively with volumetric fraction of air; it was independent of the volumetric
fraction of water. Leaf density was the chief driver of LMA
(Fig. 6b); LMA was uncorrelated with leaf thickness in the
studied leaves. Œft was strongly correlated with the density
of the leaf dry matter (Fig. 6c), and negatively correlated
with gmin (Fig. 6d), pft and ptlp (Fig. 6e). Œft was also negatively correlated with Cft (rs = 0.78; P = 0.008; rp = -0.70;
P = 0.024), but independent of Cft*.
Inter-relations of traits related to Klamina
Traits correlated with Klamina were themselves significantly
intercorrelated. Kpetiole was unrelated to most traits apart
from Klamina, although it was inversely rank-correlated with
Rt (Table 3). Leaf dimensions, water storage, and stomatal
traits were co-ordinated: leaf thickness and perimeter/area
(excluding Vitis) were rank-correlated and/or parametrically correlated with Cft*, Rt, guard cell length and SPI. Leaf
thickness was positively related to SPI; analysed allometrically, SPI µ lamina thickness2.37 ± 0.63 SE (rp = 0.66; P = 0.038).
Cft*, like Klamina, rank-correlated with prevailing leaf
irradiance.
DISCUSSION
Trait co-ordination may occur in two ways. Traits are structurally co-ordinated if they share an anatomical basis. Traits
are functionally co-ordinated if they are co-selected in a
given environment; they may be structurally independent
(Givnish 1987; Niklas 1994). For the six species studied, all
measured while growing in moist soil, Klamina, Kpetiole, 1/Rt,
lamina thickness and SPI were apparently functionally coordinated, reflecting a co-selection of traits that bear on the
ability of the leaf to support high maximum stomatal conductance (gmax) and high rates of transpiration and photosynthesis per unit area. Klamina was apparently also
structurally and/or functionally co-ordinated with lamina
perimeter/area and traits influencing leaf water storage
capacity. In contrast, Klamina was independent of traits associated with the ability of leaves to minimize water loss in
desiccating conditions (gmin) or to cope with low leaf water
potentials (ptlp, eft).
Figure 5. Co-ordination of Klamina and leaf water storage: (a) relative capacitance; (b) leaf area-specific capacitance; (c) time constant; and (d) transfer resistance. Symbols as in Fig. 2.
tolerance (Fig. 6c–e). The value of gmin varied approximately 16-fold from Hedera to Vitis (Fig. 6d). Values for gmin
were in the middle range of values for temperate herbs and
trees, with Vitis having an exceptionally high, and Hedera
Co-ordination of leaf traits associated with liquid
phase transport
In the six species, there was co-ordination among leaf traits
associated with liquid-phase water flux, Klamina, Kpetiole, and
1/Rt. The values of Kpetiole and Klamina and were higher in sun
than shade leaves, as previously reported for grapevine
© 2003 Blackwell Publishing Ltd, Plant, Cell and Environment, 26, 1343–1356
Leaf ‘hydrology’ 1351
Table 3. Correlation coefficients of leaf traits linked with Klamina
Klamina
Klamina
Kpetiole
dsf
Th
P/A
gcl
SPI
Cft*
Rt
Kpetiole
0.66
0.55
0.62
0.70
0.77
0.53
0.93
0.68
-0.80
0.45
0.12
0.28
0.23
0.33
0.12
-0.48
dsf
0.66
0.44
0.52
0.35
0.08
0.42
0.45
-0.57
Th
0.82
0.46
0.55
0.51
0.28
0.74
0.75
-0.40
P/A
0.77
0.22
0.37
0.62
0.82
0.90
0.56
-0.39
gcl
0.81
0.43
0.42
0.66
0.93
0.68
0.44
-0.43
SPI
0.93
0.52
0.56
0.79
0.87
0.92
0.75
-0.67
Cft*
0.89
0.59
0.71
0.78
0.68
0.72
0.86
Rt
-0.81
-0.67
-0.62
-0.46
-0.45
-0.55
-0.72
-0.84
-0.67
Italicized values are rs; values in normal font are rp. Bold-faced values significant at P <0.05. dsf: diffuse site factor; Th: lamina thickness; P/
A: lamina perimeter/area for leaves of mean area; gcl: guard cell length; SPI: stomatal pore area index; Cft*: leaf area-specific capacitance;
Rt: transfer resistance. For P/A, outlier Vitis was excluded.
(Schultz & Matthews 1993), and Rt was lower. Across all
leaves, Kpetiole rank-correlated with Klamina, reflecting the
serial arrangement of the petiole and leaf lamina. Additionally, Klamina correlated negatively with Rt, a possible case of
structural co-ordination, as the resistance between xylem
and mesophyll cells may be a component of the same tran-
spiration pathways through the leaf that are described by
Klamina. Rt was in the median case 28% of lamina hydraulic
resistance, and indeed, recent experiments have shown
extra-vascular resistance to be approximately -30% of leaf
hydraulic resistance (unpubl. data for A. saccharum and Q.
rubra), although other studies estimated a higher percent-
Figure 6. Co-ordination of traits relevant
to leaf drought tolerance, independent of
Klamina: (a) leaf volumetric fractions of air,
water and dry matter and (b) leaf dry mass
per area (LMA) versus leaf density; (c)
density of dry matter; (d) cuticular conductance; and (e) osmotic potential at full and
zero turgor versus modulus of elasticity.
Symbols as in Fig. 2.
© 2003 Blackwell Publishing Ltd, Plant, Cell and Environment, 26, 1343–1356
1352 L. Sack et al.
age (e.g. Martre, Cochard & Durand 2001). The high value
for Rt relative to lamina hydraulic resistance for Hedera
(60%) could correspond to its distinctive hydraulic design;
the Hedera leaf has no bundle sheath extensions, and has
an exceptionally low minor vein density, possibly indicating
a larger extra-vascular component in the transpirational
path (Wylie 1943, 1951; Sheriff & Meidner 1974).
Co-ordination of liquid phase transport traits
and gas exchange traits
For the six species, traits related to liquid phase transport
through the leaf were co-ordinated with traits related to gas
exchange per leaf area. In sun versus shade leaves and
across leaf types, Klamina was co-ordinated with both external
conditions (irradiance), and internal traits (lamina thickness and SPI) that are associated with high maximum rates
of gas exchange per leaf area. Thicker leaves are likely to
have more internal mesophyll surface area per lamina area
(Turrell 1936, 1944; Jackson 1967; Nobel, Zaragoza & Smith
1975; Chabot & Chabot 1977; James, Smith & Vogelmann
1999; but see Slaton, Hunt & Smith 2001) as well as higher
nitrogen content and more photosynthetic machinery per
area (Grubb 1984; Field & Mooney 1986; Koike 1988;
Niinemets 1999; Shipley & Lechowicz 2000), whereas SPI
is a determinant of maximum stomatal conductance
[gmax µ SPI/(stomatal depth + stomatal pore radius); Nobel
1999]. SPI scales with lamina thickness as well as with Klamina
(SPI µ lamina thickness2.37 ± 0.63 SE in this study; SPI µ lamina
thickness2.0 ± 0.17 in our analysis of published data for 84
species; rp = 0.43; P < 0.001; data from Abrams & Kubiske
1990; Bongers & Popma 1990). As both the thickness of the
lower epidermis (an approximate index of stomatal depth),
and guard cell length (linearly related to stomatal pore
radius) tend to increase linearly with lamina thickness
(thickness of lower epidermis µ lamina thickness0.92 ± 0.06 SE
for 188 species; rp = 0.44; P < 0.001; guard cell
length µ lamina thickness1.09 ± 0.096 SE for 84 species; rp = 0.34;
P < 0.001; our analysis of the data of Wylie 1951; Philpott
1953; Powers 1967; Abrams & Kubiske 1990; Bongers &
Popma 1990; Roderick et al. 1999b), higher SPI is likely to
drive a higher gmax. These correlations between Klamina and
gas exchange-related traits extend the framework of previously reported correlations between branch (and wholeplant) hydraulic conductivities, stomatal dimensions, gmax,
and mid-day rates of transpiration and photosynthesis per
leaf area (Nardini & Salleo 2000; Aasamaa & Sober 2001;
Aasamaa, Sober & Rahi 2001; Bhaskar et al. 2002; Meinzer
2002). Such relationships indicate an optimization of
hydraulic and gas exchange capacities (see Rosen 1967;
Cody 1974).
One surprising finding of this study was that stomatal
density per se is not a reliable index of Klamina or SPI, across
the study species. Whereas the higher SPI observed in sun
than shade leaves was due largely to variation in stomatal
density rather than guard cell length, across leaf types,
higher SPI was driven primarily by longer guard cells and
not by stomatal density (also true in our analysis of the data
of Bongers & Popma 1988; Abrams & Kubiske 1990). Thus,
across leaf types, stomatal density per se was unrelated to
other water flux traits, including lamina thickness (see
Beerling & Kelly 1996; also supported by our analysis of
the data of Abrams & Kubiske 1990; Bongers & Popma
1990). We note the general inverse relation of stomatal
density and guard cell length (see also Salisbury 1927;
Grubb et al. 1975; Wood 1934; Sack, Marañón & Grubb
2003). One suggested explanation is that the ratio of guard
cells to epidermal cells is roughly constant across leaves,
and that epidermal cells increase in size at the same rate as
guard cells (Salisbury 1927); thus, larger stomata would be
spaced further apart, and SPI would be constant. This geometric scaling holds as a central trend [for 84 species, stomatal density µ guard cell length-2.1 ± 0.13 SE; rp = 0.53;
P < 0.001; data of Abrams & Kubiske (1990) and Bongers
& Popma (1990)], but with extensive scatter. A weaker
scaling was found in this study, leading to substantial variation in SPI (see also Poole et al. 1996).
Water storage capacitance (Cft*) was co-ordinated with
Klamina, lamina thickness, and SPI. Apparently across the
study species there is a structural co-ordination of lamina
thickness and Cft* via the thickness of cells that contribute
to water mass per unit area (Shipley 1995; Lamont & Lamont 2000; Vendramini et al. 2002). Additionally, Klamina, Cft*
and Rt may be functionally co-ordinated. A high Cft* and
low Rt may contribute to the ability of the leaf to endure
fluctuating root supply and transpirational demand, minimizing transient fluctuations in mesophyll water potential.
A linkage between high Klamina and high Cft* might account
for the finding that at a given transpiration rate excised
leaves of high Klamina close their stomata relatively slowly
(Aasamaa & Sober 2001). This function of water storage
(analogous to that of a capacitor in an electronic circuit) is
alternative to that in semi-desert succulents; that is, for
drought survival. Notably, Cft* was uncorrelated across the
study species with drought tolerance traits such as Œft and
gmin.
Co-ordination of Klamina and lamina
perimeter/area
The co-ordination of Klamina and lamina perimeter/area in
five of the six species might be both structural and functional. Both Klamina and leaf shape may be structurally associated with the venation properties (Thoday 1931; Yang &
Tyree 1994; Jones 1995; Dengler & Kang 2001; Nardini et
al. 2001; Sack et al. 2002; Zwieniecki et al. 2002). The venation acts as an ‘irrigation system’, supplying water relatively
equitably across the lamina; the lower orders of major veins
(e.g. midrib and secondary veins) are ‘supply veins’ of low
axial resistance, whereas the higher-order veins leak relatively more to the mesophyll, and have a higher axial resistance (Canny 1990; Zwieniecki et al. 2002; Sack, Cowan &
Holbrook 2003). Thus, in more entire leaves, the larger
areas of mesophyll that are far from the supply veins may
© 2003 Blackwell Publishing Ltd, Plant, Cell and Environment, 26, 1343–1356
Leaf ‘hydrology’ 1353
be supplied with relatively low conductance, thus bringing
down the overall Klamina Further, these less well-supplied
mesophyll regions in entire leaves are prone to desiccation
under high evaporative demand or limited water supply
(Thoday 1931; Zwieniecki et al. 2002). Leaves with higher
perimeter/area, by contrast, would have all mesophyll
regions closer to supply veins. Furthermore, leaves with
higher perimeter/area tend to have a thinner boundary
layer over the bulk of the lamina, which enhances convective cooling and gas exchange at low windspeeds (Vogel
1968, 1970; Givnish 1987; Canny 1990). Vitis broke the
trend between Klamina and perimeter/area; the co-ordination
is not in all cases inherent. It is noteworthy that the Vitis
leaf is compound as a primordium, and expands into a
simple leaf, possibly indicating an ancestrally compound
leaf with a high perimeter/area (Bharathan et al. 2002).
Perimeter/area is related to perimeter2/area ¥ 1/area,
where perimeter2/area is an index of intrinsic (size-independent) shape. Thus, a high perimeter/area, and its benefits
described above, arise not only from a more complex shape
per se, but also from a smaller leaf. One previous study
(Sisó, Camarero & Gil-Pelegrín 2001) found Klamina to be
linked with ‘fractal dimension’, a correlate of perimeter2/
area (McLellan & Endler 1998), in eight Quercus species.
Our result indicates no relationship independent of leaf size.
Klamina and drought tolerance: associated or
independent?
A high Klamina may confer drought tolerance by allowing a
higher leaf water potential (yleaf) at a given transpiration
rate and soil water supply (Tsuda & Tyree 2000). However,
for the study leaves, Klamina and traits associated with water
flux were independent of traits associated with turgor maintenance at low leaf water potential. Klamina in this study was
measured for plants in moist soil, and it is possible that
during drought Klamina may decline due to xylem cavitation
(Kikuta et al. 1997; Nardini et al. 2001; Salleo et al. 2001),
and may be more closely related to drought tolerance traits.
For the six species studied Klamina was uncorrelated with pft,
ptlp, eft, lamina density, leaf dry mass per area (LMA), and
gmin. These traits are partially inter-related, suggesting coselection by desiccating conditions. eft was strongly linked
with the density of the leaf dry matter, which may reflect
denser cell walls. Leaf density, which derives from a high
volumetric fraction of dry matter, and a low volumetric
fraction of air (also see Niinemets 1999), drove LMA,
which, representing a low surface area: mass ratio, augments the effects of low gmin (Hadley & Smith 1990; Sack,
Marañón & Grubb 2003). A low LMA may also contribute
to a longer leaf lifespan (see below). Finally, eft was negatively correlated with pft and ptlp (see also Niinemets 2001),
and with gmin. Notably, sun leaves tended to show greater
modification for high water flux than shade leaves, and
simultaneously, features contributing to greater leaf
drought tolerance. Across leaf types, an independence of
leaf traits associated with water flux and those associated
with drought tolerance would explain why, in well-watered
conditions, drought-tolerant species can have gmax (and,
indeed, maximum relative growth rates) similar to or
higher than those of species confined to moist areas (Maximov 1931; Fernandez & Reynolds 2000; Sack 2000; Wright
et al. 2001).
The role of Klamina in carbon economy
Leaf hydrology has potential implications for plant carbon
economy. As shown above, Klamina may be co-ordinated with
photosynthetic rate per unit leaf area. However, Klamina may
be orthogonal to traits that are also important in carbon
economy, such as LMA, which can strongly influence photosynthetic rate per unit leaf mass (Evans 1972; Lichtenthaler 1985; Field & Mooney 1986; Koike 1988; Poorter & Van
der Werf 1998; Reich et al. 1999; Wright et al. 2001; Shipley
2002) and leaf lifespan (Nardini 2001; but see Sobrado
1998). We note that leaf lifespan and LMA are often correlated (Reich et al. 1999; Wright & Westoby 2002);
together they may thus represent an axis of variation
orthogonal to Klamina and water flux traits. Hedera, which
has a long-lived leaf, had a Klamina in the same range as the
five deciduous species. The independence of LMA and
Klamina found for the species in this study was previously
reported in two studies of other species (Tyree et al. 1999;
Salleo & Nardini 2000). However, we note that across large
species sets, lamina thickness and LMA are often positively
correlated (Shipley 1995; Niinemets 1999; Vendramini et al.
2002). Thus, if the co-ordination of Klamina and lamina thickness is general, Klamina might be loosely correlated with
LMA for large sets of species. However, because lamina
density is also a strong determinant of LMA (Witkowski &
Lamont 1991; Niinemets 1999), and it is orthogonal to
Klamina, an LMA–Klamina correlation would likely be weak at
best. For published data sets in which SPI correlated with
lamina thickness, it was unrelated to LMA (our analysis of
the data of Abrams & Kubiske 1990; Bongers & Popma
1990). Further, the relationship of Klamina and lamina thickness might shift with increasing proportions of leaf sclerenchyma (cf. Wright & Westoby 2002). Thick, long-lived
scleromorphic leaves are not expected to have proportionally higher Klamina than the deciduous species in this study.
Our understanding of leaf traits and their evolution will
be enhanced by further studies of leaf hydrology, both in
terms of mechanism, and to determine generality across
larger sets of species, in different growth conditions. There
is potential to integrate Klamina in the framework of traits
linking physiology to performance for different species
(Grubb 2002). For example, differences in the Klamina of
Quercus rubra relative to coexisting Acer species are associated with its higher gmax and photosynthetic rate per unit
leaf area (Jurik 1986; L. Sack, unpublished data). An
exciting field for study is the possible co-ordination of leaf
hydrology with characteristics of other systems and
organs, including resistance to xylem embolism, efficiency
of nutrient transport, and root uptake capacities; all of
© 2003 Blackwell Publishing Ltd, Plant, Cell and Environment, 26, 1343–1356
1354 L. Sack et al.
which contribute to overall plant performance in given
microclimates.
ACKNOWLEDGMENTS
We thank many researchers, staff and students at Harvard
Forest for facilitating the research, Truus Thomas for assistance in lab work, Michael Burns for logistic support, Geeta
Bharathan and Mel Tyree for helpful discussion, and Brendan Choat, Peter Grubb, Michael Roderick and Maciej
Zwieniecki for comments on the manuscript. This research
was supported by the Andrew W. Mellon Foundation and
the Arnold Arboretum, Harvard University (Putnam Fellowship to L.S.), and the National Science Foundation
under Grant no. 0139495.
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Received 23 December 2003; received in revised form 24 March
2003; accepted for publication 25 March 2003
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